Nonlinear Constitutive Model for Concretes at Early Ages Considering the Hydration Reaction

Hygro-thermal and hydration behaviors exist in concretes at early ages, which inevitably affect their mechanical properties. Accompanying water consumption in the concrete, there are several irreversible thermodynamic processes, including hydration heat production and strength growth. By considering coupled deformation, heat conduction, and a hydration reaction, a thermodynamically consistent continuum theory is developed for concrete at early age. At first, to satisfy the dissipation inequality, the energy dissipation caused by these irreversible processes can be tentatively described by introducing a hydration extent ℓ, so that a hydration kinetic equation considering the temperature and stress effects is established by linking the reaction rate with the concentrations of reactants. Compared to the Arrhenius linear relation between the reaction rate and chemical affinity, this nonlinear hydration kinetic equation is applicable to complex hydration reactions. Then, a fully coupled nonlinear constitutive model is constructed to interpret the thermo-chemical-mechanical interactions, whose numerical implementation is generated in commercial software ABAQUS using UEL (user-defined element) subroutines. Particularly, the model is used to predict the evolution of elastic modulus and temperature of two kinds of concretes under adiabatic testing: ordinary concrete (OC) and high performance concrete (HPC), which shows good agreement with experimental results. Furthermore, some examples are numerically studied to illustrate the interactions among mechanical deformation, hydration reaction, and heat conduction in concrete at early ages.